dgeev.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 448 行 · 第 1/3 页

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</span>      EXTERNAL           <a name="DGEBAK.132"></a><a href="dgebak.f.html#DGEBAK.1">DGEBAK</a>, <a name="DGEBAL.132"></a><a href="dgebal.f.html#DGEBAL.1">DGEBAL</a>, <a name="DGEHRD.132"></a><a href="dgehrd.f.html#DGEHRD.1">DGEHRD</a>, <a name="DHSEQR.132"></a><a href="dhseqr.f.html#DHSEQR.1">DHSEQR</a>, <a name="DLABAD.132"></a><a href="dlabad.f.html#DLABAD.1">DLABAD</a>, <a name="DLACPY.132"></a><a href="dlacpy.f.html#DLACPY.1">DLACPY</a>,
     $                   <a name="DLARTG.133"></a><a href="dlartg.f.html#DLARTG.1">DLARTG</a>, <a name="DLASCL.133"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>, <a name="DORGHR.133"></a><a href="dorghr.f.html#DORGHR.1">DORGHR</a>, DROT, DSCAL, <a name="DTREVC.133"></a><a href="dtrevc.f.html#DTREVC.1">DTREVC</a>,
     $                   <a name="XERBLA.134"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.137"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            IDAMAX, <a name="ILAENV.138"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      DOUBLE PRECISION   <a name="DLAMCH.139"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="DLANGE.139"></a><a href="dlange.f.html#DLANGE.1">DLANGE</a>, <a name="DLAPY2.139"></a><a href="dlapy2.f.html#DLAPY2.1">DLAPY2</a>, DNRM2
      EXTERNAL           <a name="LSAME.140"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, IDAMAX, <a name="ILAENV.140"></a><a href="hfy-index.html#ILAENV">ILAENV</a>, <a name="DLAMCH.140"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="DLANGE.140"></a><a href="dlange.f.html#DLANGE.1">DLANGE</a>, <a name="DLAPY2.140"></a><a href="dlapy2.f.html#DLAPY2.1">DLAPY2</a>,
     $                   DNRM2
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX, SQRT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input arguments
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      LQUERY = ( LWORK.EQ.-1 )
      WANTVL = <a name="LSAME.152"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVL, <span class="string">'V'</span> )
      WANTVR = <a name="LSAME.153"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVR, <span class="string">'V'</span> )
      IF( ( .NOT.WANTVL ) .AND. ( .NOT.<a name="LSAME.154"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVL, <span class="string">'N'</span> ) ) ) THEN
         INFO = -1
      ELSE IF( ( .NOT.WANTVR ) .AND. ( .NOT.<a name="LSAME.156"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVR, <span class="string">'N'</span> ) ) ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -5
      ELSE IF( LDVL.LT.1 .OR. ( WANTVL .AND. LDVL.LT.N ) ) THEN
         INFO = -9
      ELSE IF( LDVR.LT.1 .OR. ( WANTVR .AND. LDVR.LT.N ) ) THEN
         INFO = -11
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute workspace
</span><span class="comment">*</span><span class="comment">      (Note: Comments in the code beginning &quot;Workspace:&quot; describe the
</span><span class="comment">*</span><span class="comment">       minimal amount of workspace needed at that point in the code,
</span><span class="comment">*</span><span class="comment">       as well as the preferred amount for good performance.
</span><span class="comment">*</span><span class="comment">       NB refers to the optimal block size for the immediately
</span><span class="comment">*</span><span class="comment">       following subroutine, as returned by <a name="ILAENV.173"></a><a href="hfy-index.html#ILAENV">ILAENV</a>.
</span><span class="comment">*</span><span class="comment">       HSWORK refers to the workspace preferred by <a name="DHSEQR.174"></a><a href="dhseqr.f.html#DHSEQR.1">DHSEQR</a>, as
</span><span class="comment">*</span><span class="comment">       calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
</span><span class="comment">*</span><span class="comment">       the worst case.)
</span><span class="comment">*</span><span class="comment">
</span>      IF( INFO.EQ.0 ) THEN
         IF( N.EQ.0 ) THEN
            MINWRK = 1
            MAXWRK = 1
         ELSE
            MAXWRK = 2*N + N*<a name="ILAENV.183"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="DGEHRD.183"></a><a href="dgehrd.f.html#DGEHRD.1">DGEHRD</a>'</span>, <span class="string">' '</span>, N, 1, N, 0 )
            IF( WANTVL ) THEN
               MINWRK = 4*N
               MAXWRK = MAX( MAXWRK, 2*N + ( N - 1 )*<a name="ILAENV.186"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1,
     $                       <span class="string">'<a name="DORGHR.187"></a><a href="dorghr.f.html#DORGHR.1">DORGHR</a>'</span>, <span class="string">' '</span>, N, 1, N, -1 ) )
               CALL <a name="DHSEQR.188"></a><a href="dhseqr.f.html#DHSEQR.1">DHSEQR</a>( <span class="string">'S'</span>, <span class="string">'V'</span>, N, 1, N, A, LDA, WR, WI, VL, LDVL,
     $                WORK, -1, INFO )
               HSWORK = WORK( 1 )
               MAXWRK = MAX( MAXWRK, N + 1, N + HSWORK )
               MAXWRK = MAX( MAXWRK, 4*N )
            ELSE IF( WANTVR ) THEN
               MINWRK = 4*N
               MAXWRK = MAX( MAXWRK, 2*N + ( N - 1 )*<a name="ILAENV.195"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1,
     $                       <span class="string">'<a name="DORGHR.196"></a><a href="dorghr.f.html#DORGHR.1">DORGHR</a>'</span>, <span class="string">' '</span>, N, 1, N, -1 ) )
               CALL <a name="DHSEQR.197"></a><a href="dhseqr.f.html#DHSEQR.1">DHSEQR</a>( <span class="string">'S'</span>, <span class="string">'V'</span>, N, 1, N, A, LDA, WR, WI, VR, LDVR,
     $                WORK, -1, INFO )
               HSWORK = WORK( 1 )
               MAXWRK = MAX( MAXWRK, N + 1, N + HSWORK )
               MAXWRK = MAX( MAXWRK, 4*N )
            ELSE 
               MINWRK = 3*N
               CALL <a name="DHSEQR.204"></a><a href="dhseqr.f.html#DHSEQR.1">DHSEQR</a>( <span class="string">'E'</span>, <span class="string">'N'</span>, N, 1, N, A, LDA, WR, WI, VR, LDVR,
     $                WORK, -1, INFO )
               HSWORK = WORK( 1 )
               MAXWRK = MAX( MAXWRK, N + 1, N + HSWORK )
            END IF
            MAXWRK = MAX( MAXWRK, MINWRK )
         END IF
         WORK( 1 ) = MAXWRK
<span class="comment">*</span><span class="comment">
</span>         IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
            INFO = -13
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.219"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DGEEV.219"></a><a href="dgeev.f.html#DGEEV.1">DGEEV</a> '</span>, -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Get machine constants
</span><span class="comment">*</span><span class="comment">
</span>      EPS = <a name="DLAMCH.232"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'P'</span> )
      SMLNUM = <a name="DLAMCH.233"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'S'</span> )
      BIGNUM = ONE / SMLNUM
      CALL <a name="DLABAD.235"></a><a href="dlabad.f.html#DLABAD.1">DLABAD</a>( SMLNUM, BIGNUM )
      SMLNUM = SQRT( SMLNUM ) / EPS
      BIGNUM = ONE / SMLNUM
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Scale A if max element outside range [SMLNUM,BIGNUM]
</span><span class="comment">*</span><span class="comment">
</span>      ANRM = <a name="DLANGE.241"></a><a href="dlange.f.html#DLANGE.1">DLANGE</a>( <span class="string">'M'</span>, N, N, A, LDA, DUM )
      SCALEA = .FALSE.
      IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
         SCALEA = .TRUE.
         CSCALE = SMLNUM
      ELSE IF( ANRM.GT.BIGNUM ) THEN
         SCALEA = .TRUE.
         CSCALE = BIGNUM
      END IF
      IF( SCALEA )
     $   CALL <a name="DLASCL.251"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRM, CSCALE, N, N, A, LDA, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Balance the matrix
</span><span class="comment">*</span><span class="comment">     (Workspace: need N)
</span><span class="comment">*</span><span class="comment">
</span>      IBAL = 1
      CALL <a name="DGEBAL.257"></a><a href="dgebal.f.html#DGEBAL.1">DGEBAL</a>( <span class="string">'B'</span>, N, A, LDA, ILO, IHI, WORK( IBAL ), IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Reduce to upper Hessenberg form
</span><span class="comment">*</span><span class="comment">     (Workspace: need 3*N, prefer 2*N+N*NB)
</span><span class="comment">*</span><span class="comment">
</span>      ITAU = IBAL + N
      IWRK = ITAU + N
      CALL <a name="DGEHRD.264"></a><a href="dgehrd.f.html#DGEHRD.1">DGEHRD</a>( N, ILO, IHI, A, LDA, WORK( ITAU ), WORK( IWRK ),
     $             LWORK-IWRK+1, IERR )
<span class="comment">*</span><span class="comment">
</span>      IF( WANTVL ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Want left eigenvectors
</span><span class="comment">*</span><span class="comment">        Copy Householder vectors to VL
</span><span class="comment">*</span><span class="comment">
</span>         SIDE = <span class="string">'L'</span>
         CALL <a name="DLACPY.273"></a><a href="dlacpy.f.html#DLACPY.1">DLACPY</a>( <span class="string">'L'</span>, N, N, A, LDA, VL, LDVL )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Generate orthogonal matrix in VL
</span><span class="comment">*</span><span class="comment">        (Workspace: need 3*N-1, prefer 2*N+(N-1)*NB)
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="DORGHR.278"></a><a href="dorghr.f.html#DORGHR.1">DORGHR</a>( N, ILO, IHI, VL, LDVL, WORK( ITAU ), WORK( IWRK ),
     $                LWORK-IWRK+1, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Perform QR iteration, accumulating Schur vectors in VL
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